パイロクロア型イリジウム酸化物で直接観測する{フェルミノード状態
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Zk(111)
Pr=2Irk(111)
0.31
Å–12O
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EDC
EDC
0.2
KW
1.0Pr2Ir2O7 ¢©ÖA:]N5´3y!ÆÓÃ£&ÆÓÃÉ¹ÐÌE ARTICLE
NATURE| DOI: 10.1038/ncomms10042
ARTIC–0.2 0.0–0.2
0.0 COMMUNICATIONSNATURECOMMUNICATIONS| DOI: 10.1038/ncomms10042
kx
0.1
T=F¢4²×r_mF´3
É¹ÐÌÅÔÃH0,Pxy!Z¢115 K
0.0 Fermi
0.5±X
Comparison
between results
ARPESandresults
band calculat
Comparison
between ARPES
bandandcalculations.
anodeH0<-³²>RW¨[?°
a50 K £°zÉ¹ÐÌD
kk Z
Z3b, we ourcompareour experimental
resultsnear
In Fig. 3b,InweFig.
compareexperimental
results near
G withtheG wit
100 K–0.1
ab initio dispersion(greywhichcurve),
has quadratica purely quad
ab initio dispersion(grey curve),
haswhicha purely
Pr2Ir150­¡Sh³Gj£¡Q°³²2OK7 ©ÂËÑ¿»Ð\^EDC / FD
EDC / FD
L 39 eV
2. e(k)pk
L 39 eVshapeof the electronic
structure
given byt
shapeof theelectronic
structure givenby e(k)pk
Close to2. EClose
k0.0F,Γ kΓ
X W
WeV X we find anweagreement
Γ 52 eV L X 52¨,PxÆÔ¿ÎÓ¢±6¥,PxÂËÑ¿»Ðt!P|ÂËÑ¿»Ð–0.1
0.0–0.3 –0.2 –0.1
0.0find an agreement
betweenthe two, demonstrating
between thetwo, demonstratingthat the tha
curve (light-bluedottedline)tofits
to withour dataK W
quadratic quadraticcurve (light-bluedotted line)
fits wellourwelldata(eV)
Wave number,
Energy (eV)K Wk \^Ò·Ðu't!ÀÈÓªL(ÊÔÐH0}´MI²B
the samemass,effective
m0eff(m¼06.3m
thea mass
almost thealmost
same effective
meffmass,¼ 6.3mis themass
0 (m0 is offreeelectron).
On
the
other
hand,
forenergy
below" 0.01freeelectron).
On
the
other
hand,
forenergy
below"0.012eV,
EDCk / FDkNATURE COMMUNICATIONS | DOI: 10.1038/ncomms10042
Gj£f²~{the measureddeviates remarkably
from the para
the measured
dispersiondispersion
deviates remarkably
from the parabolic
Sym. EDCLowHighLow
Energy (eV){ { ³¬¢¨G.RW¨¥a©y!Px£ÀÈÓkoP

(111)

(111)

yy{ (a){ kZbbx

Highx

shape.
This contrasts
to the calculation,
which withmatches(m* = 6.3me)eV shape. This
contrasts
to the calculation,
which matches(c)c Fitting
h! = 39 eV h! = 392
2h! = (b)52 eV h! = 52 eVc

0.2

kx (Å–1)

0.2

Energy (eV)kx (Å–1)kx (Å–1)

Energy (eV)0.00

Fermi node

Energy (eV)kx (Å–1)

Energy (eV)Energy (eV)

0.4

0.4(111)

Energy (eV)Intensity

Intensity

Intensity[1] T. Kondo et al., Nat. commn. 6, 10042 (2015).
[2] M. Nakayama, T. Kondo et al., Phys. Rev. Lett. 117, 056403(2016).
Intensity

K

Energy (eV)e(k)pkup higher
to muchhigherenergies.
binding Itenergies.
It isthatpossiblee(k)pk up
to muchbinding
is possible(a)deviation
Ocorrelation
theeffects thebeyond
the deviationis Pr
dueeffects beyond
band the2Irto
2is7due to correlation
18 eV
calculation.
Intriguingly,
the total bandwidth
in the sideoccupiedcalculation.
Intriguingly,
the total bandwidth
in the occupied
0.2L
0.2(b,c)14 eVisestimated
tobe
B40
meV
(arrowsinFig.
4f,g),
18eV
isestimated
tobe
B40
meV
(arrowsinFig.
4f,g),
which
is whi–0.02
Γ
L
0.0 L
0.0
0.0 ΓΓ
L 18 eV0.0
12 eV
actuallymuch narrower
thatmeV)(4100of theXΓ
actually muchnarrower
than that than
(4100of meV)the band10eVΓLΓ 10 eV–0.2–0.2
KW
Fig. Supplementary
2g and Supplementary9e,h).
calculationcalculation(see Fig. (see2g andFig. 9e,h).Fig.
BandX
kx
–0.2
–0.04 –0.2
K W
–0.4
–0.4
ARPES
narrowing
relativeto thefunctional
density functional
theoryisa indenarrowing
relativetothedensitytheoryisindeed–0.4 –0.2
0.00.2well-known
characteristicof correlatedcharacteristicof correlated
electrons. electrons.
If that isIf th0.4 –0.4 –0.2 –0.4
–0.2
0.00.2well-known
0.4–1–0.4
0.0 –0.4 0.4 0.0
0.0
0.2
0.4(d)however, the agreement of the effective mass arouky (Å )–1
the case,kxky (Å–1)
ky (Å–1) the case, however, the agreement of the effective mass around G
ky (Å–1)ky (Å )
betweenthe dataand calculation
be a coincidence.
between thedata andcalculation
would be woulda coincidence.
ThisLowHighk(111)(Å–1)
is understandable,consideringthat theband
shapeis understandable,consideringthat the band
shapeof Pr
2Ir2Oof
7 Pr2IdeΓ
de(d)
(e)
–0.2
with comparable
energyscalesthebetweenthe spin–orbit
with comparable
energy scales
betweenspin–orbit
interactionintera
0.00.2Fermi node
0.04
and the correlations
electron correlations
is sensitive
to differentcand the electron
is sensitive
to different
calcu0.0
0.0
0.0
0.0
ARPES
(e)(seeARPES
lation methods
Supplementary
4; Suppleme
lation methods(see Supplementary
Note 4; Note
Supplementary
0.00
0.02
Figs 1 andFigs
9). 1 and 9).
Γ causeAnotherpossiblecause
of the discrepancy
between
Anotherpossibleof thediscrepancy
between thedata the–0.1
–0.1
–0.1
–0.1
and
calculations
is (T=70K)
thestrongof
coupling
of toelectrons
to the boandcalculations
is the strong
coupling
electrons
the bosonic
0.00
Γmodes,could significantly
renormalize
the band s–0.3 0.0 0.3 –0.3 0.0 0.3–0.3–0.3 0.0
0.3 whichmodes,
alsowhichcouldalsosignificantly
renormalize
the band shape.
–0.4 0.0 0.4–0.4–0.30.0
0.0 0.4
0.3–0.30.0
0.00.30.3
–1–1
–1
–1–1
–1
–1
Indeed,thepeak–dip–humpshape,
which
isa
charactekyk(Å)
k(Å)
k(Å)
k(Å)
Indeed,thepeak–dip–humpshape,
whichisacharacteristicky (Å–1)
(Å)
k(Å)
k(Å)
xyx
yx
–0.04
–0.02 xtting (m* = 6.3me)strongmode coupling,
seen inEDCs
signature signatureof strong ofmode
coupling,
is seen inisEDCs(Fig.
3e), (Figand calc.
10eV fg
being consistent
this scenario.
One of candidates
g ~/40EDC
FDat 75 K meV ~ 40 meV
being consistent
with this withscenario.
One of candidatesfor the fo
50 K 0.2
100 K f9eV 150
75 K
meV ~ 40 meV
meV ~ ~4040meV~ 40KmeV ~ ~4040meV
0.0
–0.04
–0.2
bosonicmodesis the phonons,
which
are
usuallytocoupledtbosonicmodes
isthephonons,
which
are
usuallycoupled
the8eV0.0 –0.1 0.0
k 0.0
7eV)
0.0kx(Å–1–0.1
0.0 –0.1–0.1–0.4 –0.2
0.00.2x (Å 0.0systems
very Anotherstrongly. candidate
Another candidate
is sugg
correlatedcorrelated
systems verystrongly.
is suggested–10.2–1ky (Å )Energy (eV) )by the similarityof the distorted
slightly distorted
bandto shapby the similarityof the slightly
band shapemeasurements
in graphene,
whereit was attributed
to electmeasurements
in graphene,
where it wasattributed
to electron–
9 eV
10 eV (Γ)
EDC
Sym EDC h! =24 Namely, the origin could be the same i
plasmon24coupling. Namely, .theorigin could be the same in theplasmon couplingeV (L) Temperature variation of FD-divided EDCs measured atES spectra and evidence for the Fermi nodal state.18(a,b)
cases:ofemissionof modescollectivemodesverticalthroughvertical intertwo cases: twoemission
collective
throughinterband
respectively. In d, the observed k points for a and b14arelines, respectively.
transitions
becomesabove
possibleabove a thresholdenergy, modi
becomes possiblea thresholdenergy, modifying
eV marked by purple and orange dashed transitions
the spectrum.
he energy of 3kBT. The spectral peak positions are marked by coloured circles. The original EDCs
usedtheforspectrum.
the111)Z

12 deVwith a light-blue arrow measured at various temperatures.
D-divided EDCs along a momentum cut indicated in
10 eV (Γ)
y red bars and dashed curves. The Fermi node is marked by a magenta circle. At T ¼ 150 K, the Correlation-driven
spectral peaks
are anomalous
Correlation-driven
anomaloustemperaturetemperature
evolution.evolution.
The